The causal automorphisms (≤- automorphisms) of ℝn, n > 2, are known to be orthochronous Lorentz transformations up to scale factors. The result fails in case n = 2. Bijective mappings that map light cones onto light cones are also known to be Lorentz transformations (up to scale factors) in case n > 2. This result fails as well for n = 2. Our result (including previous ones) is that invariance of the pseudo-euclidean distance 1 characterizes Lorentz transformations for n ≥ 2. For n = 2 the distance 1 can be replaced by each distance ρ ≠ 0 (in case n > 2 by ρ > 0).